@inproceedings{2270,
  abstract     = {Representation languages for coalitional games are a key research area in algorithmic game theory.   There is an inher-
ent tradeoff between how general a language is, allowing it to  capture  more  elaborate  games,  and  how  hard  it  is  computationally to optimize and solve such games.  One prominent  such  language  is  the  simple  yet  expressive
Weighted Graph Games  (WGGs) representation (Deng  and Papadimitriou 1994), which maintains knowledge about synergies between agents in the form of an edge weighted graph. We  consider  the  problem  of  finding  the  optimal  coalition structure in WGGs. The agents in such games are vertices in a graph, and the value of a coalition is the sum of the weights of the edges present between coalition members. The optimal coalition structure is a partition of the agents to coalitions, that maximizes the sum of utilities obtained by the coalitions. We  show  that  finding  the  optimal  coalition  structure  is  not only hard for general graphs,  but is also intractable for restricted families such as planar graphs which are amenable for many other combinatorial problems.  We then provide algorithms with constant factor approximations for planar, minorfree and bounded degree graphs.},
  author       = {Bachrach, Yoram and Kohli, Pushmeet and Kolmogorov, Vladimir and Zadimoghaddam, Morteza},
  location     = {Bellevue, WA, United States},
  pages        = {81--87},
  publisher    = {AAAI Press},
  title        = {{Optimal Coalition Structures in Cooperative Graph Games}},
  year         = {2013},
}